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Question
Solve the following system of inequalities graphically.
4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0
Solution
To find graphical solution, construct the table as follows:
| Inequation | Equation | Double Intercept form |
Points (x, y) |
Region |
| 4x + 3y ≤ 60 | 4x + 3y = 60 | `"x"/15 + "y"/20` = 1 | A (15, 0), B (0, 20) |
4(0) + 3(0) ≤ 60 ∴ 0 ≤ 60 ∴ origin side |
| y ≥ 2x | y = 2x | – | O (0, 0), C (10, 20) |
0 ≥ 2(0) ∴ 0 ≥ 0 ∴ origin side |
| x ≥ 3 | x = 3 | – | – | 0 `≱ ` 3 ∴ R.H.S. of the line x = 3 |
| x ≥ 0 | x = 0 | – | – | R.H.S. of Y-axis |
| y ≥ 0 | y = 0 | – | – | Above X-axis |
The shaded portion represents the graphical solution.
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